A method for predicting high-cycle fatigue limit of additively repaired components considering defect characteristics

Abstract

The application discloses a kind of high-cycle fatigue limit prediction methods of additive repair component considering defect characteristics, obtain the defect characteristics of repair area of additive repair simulation component, and the defect-fatigue life model considering additive repair defect is established based on the defect characteristics of repair area;Obtain the defect characteristics and material parameters of additive repair component, and establish the finite element model of additive repair component;The defect-fatigue life model is corrected to fatigue fracture phase field model by local stress-strain method, and a high-cycle fatigue limit prediction model is established;According to the high-cycle fatigue limit prediction model, the life of the additive repair component is predicted.The defect characteristic parameters after being integrated with additive repair can more accurately predict the high-cycle fatigue limit of additive repair titanium alloy simulation blade.

Description

Technical Field

[0001] The present invention relates to structural fatigue life prediction, and in particular to a method for predicting the high-cycle fatigue limit of an additively repaired component taking defect characteristics into consideration. Background Art

[0002] Engine fans and low-pressure compressors commonly utilize an integral blisk design. During service, blisk blades are subjected to the combined effects of centrifugal forces from high rotational speeds and vibration stresses caused by airflow excitation. Damage to these blades significantly reduces their fatigue strength. Traditional repair methods typically employ techniques such as grinding and welding to reduce local stress concentrations or repair geometric dimensions, restoring blade fatigue performance. However, these methods are unable to address issues such as chipped corners and large gaps. Currently, additive manufacturing technology has been applied to the repair of fan / compressor blades, enabling installation and deployment.

[0003] Porosity, lack of fusion defects, and residual tensile stresses generated during the additive repair process can affect the fatigue performance of repaired components. This leads to unclear high-cycle fatigue damage mechanisms in additively repaired blades, making it difficult to develop fatigue prediction models and accurately assessing the fatigue performance of repaired blades. Defect characteristics primarily include defect area (volume), sphericity, aspect ratio, porosity, defect location, and defect type (pores, LOF). These parameters significantly influence the fatigue performance and fatigue crack growth behavior of AM components. Therefore, researchers have investigated the relationship between additive defects and component fatigue performance and, based on experimental data on defect-fatigue life, have proposed a number of methods for modifying the SN curve prediction models for defect-free metals. These include the stress intensity factor-fatigue life model, the X-Nf model, the Z-Nf model, and a modified SWT model. These models correct the numerical calculations of SN fatigue life for conventional metals and improve the accuracy of fatigue life simulations for defect-containing specimens. The fatigue life of additively repaired components is also highly correlated with crack growth at the defect site, making it crucial to develop a realistic model describing the fatigue crack growth process based on fracture mechanics theory. Summary of the Invention

[0004] Purpose of the invention: In view of the above shortcomings, the present invention provides a method for predicting the high-cycle fatigue limit of additively repaired components by taking into account defect characteristics to improve prediction accuracy.

[0005] Technical solution: To solve the above problems, the present invention adopts a method for predicting the high-cycle fatigue limit of additively repaired components taking into account defect characteristics, comprising the following steps:

[0006] Step 1: Obtain the defect characteristics of the repaired area of ​​the additive repair simulation component, and establish a defect-fatigue life model considering the additive repair defects based on the defect characteristics of the repaired area;

[0007] Step 2: Obtain the defect characteristics and material parameters of the additively repaired component and establish a finite element model of the additively repaired component;

[0008] Step 3: Modify the fatigue fracture phase field model using the defect-fatigue life model through the local stress-strain method to establish a high-cycle fatigue limit prediction model;

[0009] Step 4: Based on the high cycle fatigue limit prediction model, the life of the additively repaired component is predicted.

[0010] Furthermore, the additive repair simulation component is ground and polished, sliced ​​and sampled, and CT scanned to obtain the defect characteristics of the repair area, which include defect size, defect location, and defect morphology.

[0011] Furthermore, the statistical probability distribution of defect size, defect location, and defect morphology in the repaired area of ​​the additive repair simulation component is integrated into the classical fatigue theory to establish a defect-fatigue life model that takes additive repair defects into account:

[0012]

[0013]

[0014] Among them, σ max ΔΩ represents the fatigue damage parameter of the defect, which is the maximum stress σ max The product of the defect characteristic value ΔΩ; N f represents the fatigue cycle life; α2 and β2 are the fitting parameters of the defect fatigue life model, Y represents the defect type, represents the equivalent circular area of ​​the defect, η represents the sensitivity of the material fatigue life to the defect size, α represents the sensitivity of the material fatigue life to the defect sphericity, β represents the sensitivity of the material fatigue life to the defect position, D l Indicates the defect location, C d Indicates roundness.

[0015] Furthermore, the defect size is represented by the volume of the sphere or circular area that encloses the entire defect; the defect position D is represented by the normalized distance from the surface of the simulated component; the defect morphology is represented by the roundness C d To express;

[0016]

[0017]

[0018] Among them, D f is the thickness of the simulated component, D dis the shortest distance from the defect to the surface of the simulated component; A is the equivalent area of ​​the defect, and L is the perimeter of the defect.

[0019] Furthermore, the phase-field method was used to calculate the high-cycle fatigue limit of additively repaired components. Its characteristic is that it describes cracks using continuous order parameters, eliminating the need to numerically track discontinuities in the displacement field. For example, a crack is represented by a phase-field variable d that varies between 0 and 1. If the material is intact, d = 1; if a crack is present, d = 0. Therefore, the variable d can be considered a damage variable in an elastic damage model.

[0020] The governing equations of the fracture phase field problem are described as follows:

[0021]

[0022] Where L is the time term coefficient and ψ is the Helmholtz free energy density.

[0023] In the brittle phase field fracture model, the crack order parameter is d. Based on the small deformation assumption, the total energy functional can be written as:

[0024]

[0025] Where g(d) is the decay function, ψ e (ε) is the elastic energy, G c is the fracture toughness of the material, is the total configuration energy, including the local free energy and gradient energy of the crack.

[0026] The crack configuration energy expression is:

[0027]

[0028] Where l is the characteristic length of the crack, represents the gradient operator, and the right side of the above formula represents the gradient energy.

[0029] The decomposition method uses strain volume deviator decomposition:

[0030]

[0031] where ε represents the total strain, ε S is the volumetric strain, ε D is the bias strain, ε S =1 / 2tr(ε),ε D =ε-1 / 2tr(ε).

[0032] The elastic strain energy is:

[0033]

[0034] Where K = λ + μ, where λ and μ are the material's Lame constants, and tr represents the matrix trace. Here, the strain energy is decomposed into tension and compression, and compressive stress does not provide a crack driving force.

[0035] When mechanical parts are subjected to alternating loads, although the stress level is lower than the yield limit of the material, they may still experience sudden brittle fracture after a long period of repeated stress cycles. This phenomenon is called fatigue fracture. Based on the phase field fracture free energy, the fatigue attenuation function α(D) is introduced to calculate the phase field fracture toughness G. c Interpolation is performed to consider the effect of fatigue cyclic loading on crack growth. When the material is subjected to cyclic loading, the fatigue attenuation function decreases. The fracture toughness of the material decreases, and the crack begins to grow. The total free energy equation at this time can be rewritten as:

[0036]

[0037] Fatigue attenuation function acts on fracture toughness G c α(D) is a monotonically decreasing function from 0 to 1, which decreases with the increase of fatigue damage D.

[0038] Considering quasi-static loading, the governing equation of the crack d-order parameter can be obtained according to the minimum energy method:

[0039]

[0040] In addition, an irreversible condition must be added to prevent the release of elastic energy after unloading, which leads to crack healing. Based on a very simple and effective solution to crack healing proposed by Miehe et al., a history variable is introduced:

[0041]

[0042] It means that the crack driving force is the maximum tensile elastic energy in history. Replace the elastic energy ψ with H(x,t) e + , which means that after unloading, the driving force still maintains the maximum value from loading to the current moment, thus preventing the crack from healing. Therefore, the governing equation of the order parameter can be written as:

[0043]

[0044] Where d is the phase field variable of the crack that varies between 0 and 1, l is the characteristic length of the crack, Δd is the Laplace operator of the phase field variable, and Π is the total energy;

[0045] The fatigue attenuation function α(D) is:

[0046] α(D)=(1-α0)(1-D) ξ +α0

[0047] Where α0 is the minimum fatigue attenuation coefficient and ξ is the fatigue attenuation exponent. This defect-fatigue life model is incorporated into the fatigue fracture phase field model using the local stress-strain method. The fatigue damage parameters and fatigue damage variables are calculated using historical variables and the Miner damage accumulation criterion.

[0048] Based on the defect-fatigue life model, the fatigue life of the additively repaired component in a single cycle is calculated. The fatigue damage parameter D is calculated based on the damage accumulation criterion. The calculated damage parameter is substituted into the fatigue attenuation function to attenuate the fatigue fracture energy, thereby driving the expansion of fatigue cracks. The fatigue life of the additively repaired component is calculated based on the fatigue crack propagation life curve, and then its fatigue limit is obtained.

[0049] First, the calculation from nominal stress to local strain is performed based on the Ramberg-Osgood model theory:

[0050]

[0051] Where E is the Young's modulus of the material, ε a is the strain amplitude, K′ and n′ are the cyclic hardening strength coefficient and cyclic strain hardening exponent respectively, and the Neuber criterion is used for stress-strain conversion.

[0052] σ el ε el =σ a ε a

[0053] Where σ el ,ε el is the equivalent stress and strain, which can be automatically solved in the phase field program. Based on the above two formulas, the equivalent stress and strain amplitude can be solved. According to different stress ratios, there is a relationship

[0054] Based on the defect-fatigue life model established in step 2, the fatigue life in a single cycle is calculated using the following formula:

[0055]

[0056] The parameters in the formula are all material fatigue parameters, see Tables 1 and 2 for details. According to the above formula, the fatigue life of a single cycle N is solved. i , the damage parameter D is calculated based on Miner's damage accumulation criterion:

[0057]

[0058] When D = 1, the material is completely damaged. D represents the fatigue damage parameter. The calculated D is then substituted into the fatigue attenuation function to attenuate the fatigue fracture energy, thereby driving the growth of fatigue cracks. Finally, the fatigue life of the component is calculated based on the fatigue crack growth life curve, and thus its fatigue limit is obtained.

[0059] The present invention also adopts a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0060] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above method when executed by a processor.

[0061] Beneficial effects: Compared with the prior art, the significant advantage of the present invention is that it obtains the defect distribution of the metal material after additive manufacturing repair, integrates it into the classical fatigue theory method, and predicts the high-cycle fatigue limit of the additively repaired blade based on the fatigue fracture phase field model. The model takes into account the influence of defect size, morphology, and position on the fatigue life curve during high-cycle fatigue. By establishing a finite element model of a simulated blade with additive repair characteristics, the fatigue life and fatigue crack propagation behavior of the titanium alloy standard specimen and the simulated blade under different defect characteristic parameters are calculated. This method incorporates the defect characteristic parameters after additive repair, and can more accurately predict the high-cycle fatigue limit of the additively repaired titanium alloy simulated blade. This method is unique and novel, has a certain degree of robustness, and is expected to be extended to the calculation of high-cycle fatigue life of additively manufactured metals or additively repaired complex components. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a schematic diagram of the process of the present invention.

[0063] Figure 2 This is the additively repaired TC17 tensile fatigue specimen and finite element model in the present invention.

[0064] Figure 3 This is the damage evolution analysis of the TC17 tensile fatigue specimens repaired with additive materials at different cycle numbers in the present invention.

[0065] Figure 4 This is the SN experiment and prediction curve of the additively repaired TC17 tensile fatigue specimen in the present invention.

[0066] Figure 5 This is the blade specimen and finite element model for the additive repair of TC17 in the present invention.

[0067] Figure 6 Schematic diagram of the additive repair area and substrate of the blade simulated by the additive repair TC17 in the present invention.

[0068] Figure 7 Schematic diagram of fatigue crack propagation in the TC17 simulated blade using additive repair in the present invention. DETAILED DESCRIPTION

[0069] like Figure 1 As shown, the method for predicting the high-cycle fatigue limit of an additively repaired component considering defect characteristics in this embodiment includes the following steps:

[0070] Step 1: Perform laser additive repair tests on titanium alloy simulated blades and standard tensile fatigue tests. Grind and polish the simulated blades and standard specimens after additive repair. Use the defect data of the additively repaired TC17 titanium alloy tensile fatigue specimens obtained by CT testing and the SN curve of the additively repaired TC17 titanium alloy measured under tension-tension fatigue load to perform parameter fitting on the finite element model. The data used for model fitting are shown in Table 1.

[0071] Table 1 SN curve fitting of additively repaired TC17 titanium alloy

[0072]

[0073] Step 2: Based on the statistical probability distribution of defect size, location, and morphology of the repaired area after laser additive repair, the defect size, location, and morphology are integrated into the classical fatigue theory to establish a fatigue life model that takes additive repair defects into account. The least squares method is used to fit the defect fatigue life model parameters to achieve the best fitting effect. The defect parameters and fatigue life data are shown in Table 1, and the SN curve obtained by fitting is shown in Figure 4 In the figure, the defect fatigue damage parameter is the vertical axis, and the value is the formula The left part of the figure is shown in Table 2. By fitting, we can get α2 = 2440 MPa and β2 = -0.09.

[0074] Table 2 Defect-life model parameters for additive repair of TC17 titanium alloy

[0075]

[0076]

[0077] Step 3: Based on the laser additive repair test, a finite element model of the blade was established. The additive repair area and the base area were distinguished according to the experimental results (mechanical behavior test, residual stress, microhardness). Figure 5 The characteristic parameters of defects in the additively repaired area and the substrate area are shown in Table 2. It can be seen that the defect size, location, and sphericity of the additively repaired area are all inferior to those of the substrate. The simulation values ​​are consistent with the experimental results, indicating that the more numerous and larger the defects are after additive repair, the greater the hazard. Therefore, fatigue cracks typically initiate and propagate in the additively repaired area.

[0078] Step 4: Based on the traditional local stress-strain method and fatigue fracture phase field theory, a high-cycle fatigue limit prediction model is established. Combined with the residual alternating solution strategy and the fatigue envelope loading method, batch calculation of high-cycle fatigue extension problems at the component level (simulated blades) is achieved. The finite element model and loading diagram are shown in Figure 2 and Figure 5 , see step 5 for specific loading parameters and model parameters.

[0079] Step 5: The additive repair defect-fatigue life model of step 2 and the additive repair blade finite element model established in step 3 are transferred to the high-cycle fatigue limit prediction model established in step 4 to achieve high-precision prediction of the high-cycle fatigue limit of the laser additive repaired blade.

[0080] The specific implementation steps are as follows: first, a standard tensile fatigue additive repair model is established to obtain a quasi-two-dimensional finite element model considering defects as shown below. The size of the finite element model is consistent with the size of the actual sample, where the minimum grid size is 0.25mm, and the fatigue fracture phase field parameter is G c =32GPa / m, l0=1mm. The finite element model of the additively repaired TC17 titanium alloy tensile fatigue specimen is shown in Figure 2. Figure 2 As shown in Figure 2, numerical model parameters are differentiated based on fatigue life test results. After additive repair, the Young's modulus of the additive area decreases. Based on CT test results, defects in the matrix area are set to be extremely small with high sphericity, while defects in the additive area are set to be smaller with high sphericity. Specific parameters are shown in Table 2.

[0081] Based on the constructed defect-fatigue life finite element model, the numerical simulation calculation of the SN curve of the additively repaired TC17 titanium alloy under tension-tension fatigue load was carried out. The load state was set to stress ratio R = 0.1 and the maximum stress σ max =440MPa. The stress-strain contours reveal stress concentration at the interface between the additively repaired area and the substrate, with maximum stress occurring on the specimen surface. The defect fatigue damage parameters are concentrated in the additively repaired area, differing significantly from those in the substrate. Furthermore, as the number of cycles increases, the maximum fatigue damage parameter shifts toward the center of the specimen. This phenomenon is attributed to differences in defect characteristic parameters between the substrate and additively repaired areas.

[0082] Figure 3The fatigue damage variables and crack evolution under different numbers of cycles show that the fatigue damage is concentrated inside the additive repair area and gradually accumulates to 1 as the number of cycles increases. At this time, the fracture toughness decreases at the position where the fatigue damage parameter accumulates to 1, and the crack initiates from the center of the specimen and expands rapidly. This is consistent with the observation results of the macro crack position of the sample after fatigue testing and the position of the crack source on the fatigue fracture. In the SN curve calculation, the fatigue life of the tension-tension fatigue specimen is mainly contributed by the crack initiation life. The crack propagation life is not considered here, and its initiation life is regarded as the total fatigue life for calculation. From this, it can be calculated that the fatigue life of this additive repaired specimen (R=0.1, σ max =440MPa) has a fatigue life of approximately 55,000 cycles.

[0083] The fatigue life of the additively repaired TC17 titanium alloy under different loads was numerically calculated using the above method. Six sets of parameters were set with maximum stress of 250MPa, 300MPa, 350MPa, 400MPa, 440MPa, and 500MPa and stress ratio of 0.1. The fatigue life was numerically calculated using the above method, and the predicted data of SN was obtained as follows: Figure 4 Because the numerical simulation model takes into account the characteristics of additive manufacturing defects, the finite element simulation results are almost completely consistent with the fitting curve of the experimental results, demonstrating that the model can fully account for the impact of defects in additively repaired components on fatigue life. Furthermore, this model enables quantitative calculation of the impact of defect characteristics on fatigue life, providing a research tool for studying the differences in defect distribution caused by different additive repair processes and supporting the simulation of high-cycle fatigue of blades using additive repair.

[0084] Figure 5 The diagram of the blade simulated by additive repair, the finite element model and the loading diagram are shown. The present invention sets an additive repair area in the lower right corner of the simulated blade, with a semicircular groove with a radius of 3mm and a distance of 10mm between the groove center and the clamping end. The rest of the body is the base. The material parameters follow the standard tensile fatigue simulation data to ensure data consistency. The simulation results are shown in Figure 1. Figure 7 Under fatigue load, cracks initiated at the surface blade root of the additively repaired area, where the fatigue limit was measured to be approximately 325 MPa, which is within the experimental measurement range. The fatigue crack initiation location is also consistent with the experimental results, further proving the correctness of this method.

Claims

1. A method for predicting the high-cycle fatigue limit of an additively repaired component taking into account defect characteristics, characterized in that: The following steps are involved: Step 1: Obtain the defect characteristics of the repaired area of ​​the additive repair simulation component, and establish a defect-fatigue life model that takes into account the defects of the additive repair based on the defect characteristics of the repaired area; integrate the statistical probability distribution of defect size, defect location and defect morphology of the repaired area of ​​the additive repair simulation component into the classical fatigue theory to establish a defect-fatigue life model that takes into account the defects of the additive repair: Among them, σ max ΔΩ represents the fatigue damage parameter of the defect, which is the maximum stress σ max The product of the defect characteristic value ΔΩ; N f represents the fatigue cycle life; α2 and β2 are the fitting parameters of the defect fatigue life model, Y represents the defect type, represents the equivalent circular area of ​​the defect, η represents the sensitivity of the material fatigue life to the defect size, α represents the sensitivity of the material fatigue life to the defect sphericity, β represents the sensitivity of the material fatigue life to the defect position, D l Indicates the defect location, C d Indicates roundness; Step 2: Obtain the defect characteristics and material parameters of the additively repaired component and establish a finite element model of the additively repaired component; Step 3: Modify the fatigue fracture phase field model using the defect-fatigue life model through the local stress-strain method to establish a high-cycle fatigue limit prediction model; Step 4: Based on the high cycle fatigue limit prediction model, the life of the additively repaired component is predicted.

2. The method for predicting the high cycle fatigue limit of an additively repaired component according to claim 1, characterized in that: The additive repair simulation component is ground and polished, sliced ​​and sampled, and CT scanned to obtain the defect characteristics of the repair area, which include defect size, defect location, and defect morphology.

3. The method for predicting the high cycle fatigue limit of an additively repaired component according to claim 2, characterized in that: The defect size is represented by the volume of a sphere or circular area that encloses the entire defect; the defect position D is represented by the normalized distance from the surface of the simulated component; the defect morphology is represented by the roundness C d To express; Among them, D f is the thickness of the simulated component, D d is the shortest distance from the defect to the surface of the simulated component; A is the equivalent area of ​​the defect, and L is the perimeter of the defect.

4. The method for predicting the high cycle fatigue limit of an additively repaired component according to claim 1, characterized in that: The phase field method is used to calculate the high cycle fatigue limit of the additively repaired component. Based on the phase field fracture free energy, the fatigue attenuation function α(D) is introduced to calculate the phase field fracture toughness G c Interpolation is performed to consider the effect of fatigue cyclic loading on crack growth. When the material is subjected to cyclic loading, the fatigue attenuation function decreases; the fracture toughness of the material decreases, and the crack begins to grow. Based on the defect-fatigue life model, the fatigue life of the additively repaired component in a single cycle is calculated. The fatigue damage parameter D is calculated based on the damage accumulation criterion. The calculated damage parameter is substituted into the fatigue attenuation function to attenuate the fatigue fracture energy, thereby driving the expansion of fatigue cracks. The fatigue life of the additively repaired component is calculated based on the fatigue crack propagation life curve, and then its fatigue limit is obtained.

5. The method for predicting the high cycle fatigue limit of an additively repaired component according to claim 4, characterized in that: The governing equations of the phase field model are established using the minimum energy method: Where d is the phase field variable of the crack that varies between 0 and 1, l is the characteristic length of the crack, Δd is the Laplace operator of the phase field variable, and Π is the total energy; The fatigue attenuation function α(D) is: α(D)=(1-α0)(1-D) ξ +a0 Among them, α0 is the minimum fatigue attenuation coefficient, and ξ is the fatigue attenuation exponent.

6. The method for predicting the high cycle fatigue limit of an additively repaired component according to claim 5, characterized in that: The calculation formula of damage parameter D is: Among them, N i is the fatigue life of a single cycle calculated based on the defect-fatigue life model.

7. The method for predicting the high cycle fatigue limit of an additively repaired component according to claim 1, characterized in that: The local stress-strain method is: First, calculate the nominal stress to local strain: Where E is the Young's modulus of the material, ε a is the strain amplitude, K′ and n′ are the cyclic hardening strength coefficient and cyclic strain hardening exponent, σ a is stress; Then perform stress-strain conversion: s el e el =s a e a Where, σ el ,ε el is the equivalent normal stress and strain; Based on the above two formulas, the equivalent stress-strain amplitude can be solved. According to different stress ratios R, there is a relationship 8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

Images